Theorem 1 (Tarski-Seidenberg [1]}) 
Let \(S\)  be a semialgebraic set in \(\mathbb {R}^{m+n}\) , then
\(\bar{S}:=\lbrace x\in \mathbb {R}^m:(x,y)\in S \ \text{for some} \ y\in \mathbb {R}^n\rbrace \) 
